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A system consists of two components. P(the 1st component functions in satisfactory manner during its design...

A system consists of two components. P(the 1st component functions in satisfactory manner during its design life)=0.75, P(at least one of the two components functions in satisfactory manner during its design life)=0.86, and P(both component functions in satisfactory manner during its design life)=0.65. given that the second component functions in a satisfactory manner throughout its design life, What is the probability that the first one does also?

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Answer #1

We have

P(the 1st component functions in satisfactory manner during its design life)=0.75

P(both component functions in satisfactory manner during its design life)=0.65.

We asked the conditional probability that second component functions in a satisfactory manner throughout its design life, What is the probability that the first one does also

P ( 1st component functions in a satisfactory /2nd component functions in a satisfactory manner)

= P( both components function in satisfactory manner)/P( 2 nd component function in a satisfactory manner)

= 0.65/0.75

= 0.8667

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